发表机构
School of Mathematics and Statistics, Tianshui Normal University（天水师范学院数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文完整刻画了一维Noether环的iso-Artinian性质，给出四个等价条件，并解决了Daneshvar和Divaani-Aazar提出的开放问题。
AI 中文摘要
设$R$是一个一维交换Noether环，具有唯一极小素理想$\mathfrak p$，使得$D=R/\mathfrak p$是主理想整环。我们给出了此类环中iso-Artinian性质的完整刻画，即以下条件等价：$R$是iso-Artinian的；$\mathfrak pR_{\mathfrak p}=0$；$len_R(\mathfrak p)<\infty$；$\mathfrak p/\mathfrak p^2$在$D$上是挠的。作为推论，我们完全回答了Daneshvar和Divaani-Aazar的Question 3.9：在他们的假设$Min R\subsetneq Ass R$下，环是iso-Artinian的当且仅当其幂零根具有有限长度，并且环是非iso-Artinian的当且仅当其余法模具有正秩。
英文摘要
Let $R$ be a one-dimensional commutative Noetherian ring with a unique minimal prime $\mathfrak p$ such that $D=R/\mathfrak p$ is a principal ideal domain. We give a complete characterization of the iso-Artinian property in this class, that is, the following conditions are equivalent: $R$ is iso-Artinian; $\mathfrak pR_{\mathfrak p}=0$; $len_R(\mathfrak p)<\infty$; $\mathfrak p/\mathfrak p^2$ is torsion over $D$. As a consequence, we completely answer the Question~3.9 of Daneshvar and Divaani-Aazar: under their hypotheses $Min R\subsetneq Ass R$, the ring is iso-Artinian precisely when its nilradical has finite length, and it is non-iso-Artinian precisely when the conormal module has positive rank.
